It is advantageous to use an air-cooled internal combustion engine for a small outboard marine drive in view of reducing weight. The exhaust gas expelled from the engine is high in temperature, and it is therefore essential to prevent the heat from the exhaust gas from heating various parts of the outboard marine drive. According to the invention disclosed in Japanese UM publication (kokoku) No. 2-13703, a small water pump is provided in a lower end of a vertical drive shaft to feed water to an upper part of an extension case adjacent to an exhaust port. This however complicates the structure, and hence increases the manufacturing cost. Furthermore, the pump causes a corresponding loss in the output of the engine.